Expectation of Matrices
If X is an m × n matrix, then the expected value of the matrix is defined as the matrix of expected values:
![\operatorname{E} = \operatorname{E} \left [\begin{pmatrix} x_{1,1} & x_{1,2} & \cdots & x_{1,n} \\ x_{2,1} & x_{2,2} & \cdots & x_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ x_{m,1} & x_{m,2} & \cdots & x_{m,n} \end{pmatrix} \right ] = \begin{pmatrix} \operatorname{E} & \operatorname{E} & \cdots & \operatorname{E} \\ \operatorname{E} & \operatorname{E} & \cdots & \operatorname{E} \\ \vdots & \vdots & \ddots & \vdots \\ \operatorname{E} & \operatorname{E} & \cdots & \operatorname{E} \end{pmatrix}.](http://upload.wikimedia.org/math/8/e/e/8ee535192b5500d28c580c209879eb98.png)
This is utilized in covariance matrices.
Read more about this topic: Expected Value
Famous quotes containing the words expectation of and/or expectation:
“For, the expectation of gratitude is mean, and is continually punished by the total insensibility of the obliged person. It is a great happiness to get off without injury and heart-burning, from one who has had the ill luck to be served by you. It is a very onerous business, this being served, and the debtor naturally wishes to give you a slap.”
—Ralph Waldo Emerson (1803–1882)
“Sweet pliability of man’s spirit, that can at once surrender itself to illusions, which cheat expectation and sorrow of their weary moments!—long—long since had ye number’d out my days, had I not trod so great a part of them upon this enchanted ground.”
—Laurence Sterne (1713–1768)